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Given the ubiquity of non-separable optimization problems in real worlds, inthis paper we analyze and extend the large-scale version of the well-knowncooperative coevolution (CC), a divide-and-conquer black-box optimizationframework, on non-separable functions. First, we reveal empirical reasons ofwhen decomposition-based methods are preferred or not in practice on somenon-separable large-scale problems, which have not been clearly pointed out inmany previous CC papers. Then, we formalize CC to a continuous-game model viasimplification, but without losing its essential property. Different fromprevious evolutionary game theory for CC, our new model provides a much simplerbut useful viewpoint to analyze its convergence, since only the pure Nashequilibrium concept is needed and more general fitness landscapes can beexplicitly considered. Based on convergence analyses, we propose a hierarchicaldecomposition strategy for better generalization, as for any decomposition,there is a risk of getting trapped into a suboptimal Nash equilibrium. Finally,we use powerful distributed computing to accelerate it under the recentmulti-level learning framework, which combines the fine-tuning ability fromdecomposition with the invariance property of CMA-ES. Experiments on a set ofhigh-dimensional test functions validate both its search performance andscalability (w.r.t. CPU cores) on a clustering computing platform with 400 CPUcores.

Cooperative Coevolution for Non-Separable Large-Scale Black-Box Optimization: Convergence Analyses and Distributed Accelerations